I'm looking for classic references that describe the usual electrostatic contributions which have to be calculated in molecular dynamics simulations. I find it very hard to apprehend what different interaction potentials actually do to calculate electrostatic interactions.

Why do electrostatics for most potentials seem to stop at charge and dipole interactions? Shouldn't we really consider interactions involving higher-order mutipoles as well?

As you can see, I have a lot of basic holes in my knowledge of the way these calculations are carried out even though I have personally implemented some of these methods before. If someone could provide me with references that discuss the different types of approximations (and how they relate to one another) to the electrostatic part of the interactions needed for MD simulations, that would be greatly appreciated.

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    $\begingroup$ As for your second question, this is because (1) the interactions between higher-order multipoles are rather short-ranged, (2) calculating these interactions are relatively costly and more difficult to code, and (3) high-order multipoles are harder to parameterize. If you are doing ab initio calculations instead of molecular mechanics, you will see that much higher order multipoles are used (when the Coulomb interaction is calculated by multipolar expansion). For example DMol3 uses up to octupoles and hexadecapoles, and BDF uses up to 256-poles. $\endgroup$
    – wzkchem5
    Commented Jul 1, 2021 at 7:44
  • $\begingroup$ @wzkchem5 Posts are only supposed to contain a maximum of one question, so I've commented out "the first question", and if your comment answering the "second question" can be turned into an answer that would be really nice, since this has been in the unanswered queue for about 6 months! $\endgroup$ Commented Dec 25, 2021 at 21:05
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    $\begingroup$ These kinds of questions are the most useful to have answers for, but, the rarest to actually have answers for. I think it is because most people use software, they don't write/test/evaluate algorithms, so when it comes to getting references... not many people can help $\endgroup$
    – B. Kelly
    Commented Dec 25, 2021 at 21:35
  • $\begingroup$ @NikeDattani Thanks, but this question is a reference request and I'm afraid I'm not familiar with the literature in this field $\endgroup$
    – wzkchem5
    Commented Jan 3, 2022 at 10:43
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    $\begingroup$ @HemanthHaridas I am asking about things like Ewald summation/PME. I am aware that there are many different variations on Ewald summation which differ in how the transition from short to long range is handled. I wasn't aware of that when I wrote the question but that's the type of thing I'm interested in. Computing the coulomb interaction directly is trivial, so I'm interested in the more efficient ways people do it in practice. $\endgroup$
    – jheindel
    Commented Oct 17, 2023 at 17:22

2 Answers 2


The reason why most molecular force fields stop at point charges and dipoles is they're good enough.

What we mean by "good enough" is for the electrostatic potential (ESP) around a classical molecular dynamics molecule to be similar enough to the actual ESP (calculated with quantum chemistry). A definitive early article on this is Dykstra's Electrostatic interaction potentials in molecular force fields (Chem. Rev. 1993, 93, 7, 2339–2353; link). It goes into significant detail about the accuracy and cost of higher-order moments; this is not just a matter of not having enough compute (if octopoles were worth talking about in 1993 they're worth talking about now!).

This passage in particular is important:

Rather than an exact representation, we seek only one that is correct in the regions of interest. Probably the separation distances where charge field representations need to be most accurate are those from just under the separations associated with van der Waals radii to about twice that distance. ... At closer separations the charge distributions will tend to overlap and make invalid the physical justification for classical electrostatic potentials, and at separations beyond this range the interaction energy and forces are all weak; accuracy in the far-off regions is not important for most force field applications.

So the vast majority of molecular dynamics simulations are okay with point charges. Polarizable dipoles are especially valuable as a relatively cheap model for cooperative effects -- thus, polarisability can accurate capture both a relatively less bound dimer-in-vacuum and the more intensely interacting condensed phase. Higher-order moments, until now, were mostly of interest in people trying to predict IR spectra in silico. Of course, you could argue that the current wave of innovative ML models is (in roundabout way) a fitting to the higher-order near-field octo-and-beyond multiples.


Not sure whether it will satisfy all your thirst for knowledge, but you could have a look at the chapter on "Long-Range Interactions" (11 or 12, depending on edition) in "Understanding Molecular Simulation" by Frenkel & Smit.

Right at the beginning of the chapter, there is paragraph that is relevant to your question

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